Université Paris VI
Physique des Liquides et Matière Molle
Nonlinear Dynamics and Temporal Chaos (in English)

I. Dynamical Systems (pdf) (ps)
II. Convection and Lorenz Model (pdf) (ps)
III. Symmetry (pdf) (ps)
IV. Maps, Period Doubling and Floquet Theory (pdf) (ps)
V. Quasiperiodicity and Intermittency (pdf) (ps)
VI. Reaction-Diffusion Equations (pdf) (ps)
VII. Hamiltonian Systems (pdf) (ps)
VIII. Nonlinear Tourism (pdf) (ps)


Ecole Polytechnique : Instabilités et Chaos (in French)
Enseignement d'Approfondissement en Majeure de Mécanique

I. Systèmes Dynamiques (pdf) (ps)
II. Convection et Modèle de Lorenz (pdf) (ps)
III. Dédoublement de Période
IV. Ecoulements Ouverts (pdf) (ps)
V. Systèmes Hamiltoniens

A Symmetry Primer for Fluid Mechanicians
(under construction)

Reflection symmetry (pdf) (ps)
Rotations (pdf) (ps)
Complex eigenvalues (pdf) (ps)
Rectangular and centro-symmetry
Case study of channel flow

More documents

The Eckhaus instability. (pdf) (ps) Bifurcation analysis in a finite geometry.
Polar coordinates. (pdf) (ps) How to avoid singularities at the origin.
Rotating frames and fictitious forces (pdf)
Bifurcation Analysis for Time Steppers. (pdf) (ps)
How to modify a time-stepping code to calculate steady states and perform linear stability analysis.
Recursion Relations and Influence Matrices. (pdf) (ps)
Greens functions and the Sherman-Morrison-Woodbury formula.
How can systems of differential equations with coupled boundary conditions be solved? When can matrices be reduced to banded form? When do there exist recursion relations for differential operators?
Computational methods of MHD in a finite cylinder. (pdf)
Greens functions and the Sherman-Morrison-Woodbury formula.
How can systems of differential equations with coupled boundary conditions be solved? When can matrices be reduced to banded form? When do there exist recursion relations for differential operators?
In preparation
Jacobians for PDEs: matrix-free methods and preconditioning
Considering a control parameter, rather than the growth rate, as an eigenvalue.